Well, there's been an update to that. In the last 24 hours, Google has announced the launch of the new Chrome Web Store - a website that allows you to install webapps for your Google Chrome web browser. Included in that launch is dozens (if not hundreds) of webapps to choose from, some compelling, others less so.
One of the new webapps available in the Chrome Web Store is a web-based version of TweetDeck, affectionately known as ChromeDeck.
ChromeDeck has more in common with the Android and iPhone versions of TweetDeck than with the desktop version, but it's a fully-featured TweetDeck application in its own right. And, like the others, it's free.
So if you're keen to check it out, go install Google Chrome, then head over to the Web Store to see what nifty things are available.
Another important thing to note is that ChromeDeck doesn't support all the same features as HootSuite. HootSuite has some really cool tools that allow you to collaborate with members of your team, all working on the same set of Twitter accounts. But if you're not using those sorts of things, ChromeDeck is a perfectly suitable alternative that syncs with your existing TweetDeck account.